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The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics.The name originates from the replacement of certain elements in the original layout with fictitious charges, which replicates the boundary conditions of the problem (see Dirichlet boundary conditions or Neumann boundary conditions).
The charge-based formulation of the boundary element method (BEM) is a dimensionality reduction numerical technique that is used to model quasistatic electromagnetic phenomena in highly complex conducting media (targeting, e.g., the human brain) with a very large (up to approximately 1 billion) number of unknowns.
The method gained popularity for plasma simulation in the late 1950s and early 1960s by Buneman, Dawson, Hockney, Birdsall, Morse and others. In plasma physics applications, the method amounts to following the trajectories of charged particles in self-consistent electromagnetic (or electrostatic) fields computed on a fixed mesh.
This method covers the full range of electromagnetics (from static up to high frequency) and optic applications and is the basis for commercial simulation tools: CST Studio Suite developed by Computer Simulation Technology (CST AG) and Electromagnetic Simulation solutions developed by Nimbic.
This method is believed to be quick and effective, but the quality result depends on the experiment design and the time invested in it. [ 11 ] Slow galvanostatic discharge [ 11 ] : another method to evaluate the open-circuit voltage of the cell is to slowly discharge/charge it under galvanostatic conditions (i.e., at low constant currents).
The ideas behind the MFS were developed primarily by V. D. Kupradze and M. A. Alexidze in the late 1950s and early 1960s. [1] However, the method was first proposed as a computational technique much later by R. Mathon and R. L. Johnston in the late 1970s, [2] followed by a number of papers by Mathon, Johnston and Graeme Fairweather with applications.
This method couples the ensemble Monte Carlo procedure to Poisson's equation, and is the most suitable for device simulation. Typically, Poisson's equation is solved at fixed intervals to update the internal field, to reflect the internal redistribution of charge, due to the movement of carriers.
Mulliken charges arise from the Mulliken population analysis [1] [2] and provide a means of estimating partial atomic charges from calculations carried out by the methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method, and are routinely used as variables in linear regression (QSAR [3]) procedures. [4]